Optimal Operating Policies for Multi-Plant Stochastic Manufacturing Systems In a Changing Environment

This paper addresses the horizontal coordination between production units located in different countries within a supply chain in a changing environment. Our model incorporates (1) congestion and delay through uncertainties in demand and processing times, (2) a changing production cost environment through uncertainty in an environmental state (such as the exchange rate), (3) allowing production to stock, and (4) no switching costs. The main contribution of the paper is to characterize the optimal production policy as a barrier-type control policy for a series of models. For each plant, there is a barrier function defined on the environmental state that gives the total worldwide stock level barrier: this plant should be operated if and only if the stock level is below this barrier. We also show that, in a simple setting of two plants, each in different countries, the barrier functions are not always monotone in the exchange rate even when the production costs are. We present a condition under which the control barriers are shown to be monotone. Under this condition and with only two plants, it is optimal to follow a primary/secondary plant policy in which, given a fixed environmental state, it is optimal to operate both plants when stock is low, only the primary plant when stock is moderate, and neither when stock is high. Furthermore, the roles of the plants switch as the environmental state passes through the equal production cost state. In addition, the firm seeks to carry the most stock, as a hedge against future environmental state moves, when one plant is significantly cheaper than the other. The firm seeks to carry the least stock when both plants are equally costly to operate.